do I really need dedicated hosting?

I have been trying to set up a server app that creates graphics using the GD library etc.
The app comes in a number of diff flavours depending on the CPU and OS. So I got on to my hosting company and asked them what the hardware was. Unfortunately they couldn't tell me that since I am on shared hosting.
I was told I would have to get shared hosting, since I can't be sure that applications such as this will work on shared or virtual.
The thing is, this is the only reason to go to dedicated. The site doesn't get a huge amount of traffic, and there isn't a huge processor load from scripts/dbase calls.
Is there another option I do I have to go dedicated if I want this app to work?

Cheers
Ed

Found some information about dedicated hosting on this site, maybe it helps you.
http://hoster-toaster.de/root-server/
Vera